In New York, Gov. Andrew M. Cuomo vowed on Monday to introduce a bill to ban the sale of e-flavored cigarettes, and directed the state Department of Health to subpoena companies that market or sell so-called thickening agents, which are sometimes added to black market vaping products. A state laboratory, which detected the agents in vaping products collected from New York’s patients, found that they were nearly pure vitamin E acetate oil, which officials have said is a potential cause of the illnesses.

That same day, the American Medical Association called vaping “an urgent public health epidemic,” and urged people to avoid the use of any e-cigarette products until health officials learned more about the causes of the illnesses, which have remained unresolved.

The most recent death, tied to a severe lung illness believed to be related to vaping, was announced on Tuesday, in Kansas. In addition, more than 450 cases of sickness have been reported across 33 states, spurring urgent calls to action by state lawmakers.

The F.D.A. has the authority to regulate e-cigarettes federally, but e-cigarette companies do not have to submit their products to the agency for public health review until May 2020.

“This is a frightening public health phenomenon,” Mr. Cuomo said at a news conference on Monday.

In New York, at least 41 people had fallen ill as of Monday, according to the state health department — up from 34 people just four days earlier.

Video

Governor Andrew M. Cuomo of New York said the Department of Health would investigate vaping companies amid a wave of severe lung illnesses linked to its products.CreditCreditSeth Wenig/Associated Press

The flurry of proposals may indicate a shift in public opinion toward vaping, which in the early years of its popularity was often viewed — especially by teenagers — as a sleek symbol of rebellious cool. Supporters also touted it as a tool to wean smokers off traditional cigarettes.

But over the past few years, as doctors increasingly warned of addiction and the still-scarce research on the topic, government officials began to act. San Francisco in June banned not just flavored vaping products but all e-cigarettes, becoming the first city in the nation to do so. More than a dozen states prohibit vaping in public spaces where smoking is prohibited.

Attorneys general in six states are investigating e-cigarette makers related to underage use of their products.

Still, some lawmakers perceived a lack of urgency before the near-panic set off by the recent explosion of illnesses.

A bill to ban the sale of flavored e-cigarettes has been introduced in the New York State Legislature every year since 2017. The bill failed to pass before the legislative session ended in June, in part because of aggressive lobbying by the tobacco and e-cigarette industries, as well as by a coalition of adult e-cigarette users who convinced legislators to abandon the bill, said Assemblywoman Linda Rosenthal, one of the bill’s sponsors.

The effort may fare better in January, because of Mr. Cuomo’s support and the involvement of Mr. Bloomberg and his allies. Though Mr. Bloomberg did not specify which cities or states he would focus on, his foundation said in a news release that it would work with the Campaign for Tobacco-Free Kids and the Center for Disease Control over three years to end marketing practices that appeal to children, remove flavored e-cigarettes from the marketplace and pause online e-cigarette sales.

Mr. Bloomberg’s foundation has fought tobacco use around the world, funding media campaigns and encouraging bans on tobacco advertising and taxes on tobacco products.

In an opinion piece on Tuesday, Mr. Bloomberg, along with Matthew L. Myers, the head of Campaign for Tobacco-Free Kids, wrote that the battles against smoking and vaping were inextricably linked. “We know Big Tobacco’s playbook. We’ve seen this before,” the men wrote.

Ms. Rosenthal, who also plans to introduce a bill to ban all e-cigarettes until they receive F.D.A. approval, said momentum had shifted “absolutely” in favor of bans.

“People teeter between, ‘This is the right thing to do’ and ‘Maybe we should leave people to their own devices.’ But elected officials have a responsibility to protect public health,” she said. “This is a prime example of that.”

Still, vaping manufacturers have already indicated they intend to fight attempts to curtail the industry.

Austin Finan, a spokesman for Juul, said the company supported efforts to curb underage use. But he said permitting certain flavors, such as menthol, was important to helping smokers quit traditional cigarettes. Ms. Rosenthal’s bill would allow only tobacco flavoring.

The New York State Vapor Association, which represents vaping manufacturers and distributors, was less conciliatory. The group said on Monday that the governor’s blanket suggestion that people stop vaping altogether was overzealous, given the health department’s hypothesis that the sicknesses were tied to black-market products.

“If a bad batch of penicillin causes illness and death, C.D.C. doesn’t recommend people stop using all antibiotics,” Spike Babaian, a spokeswoman for the association, said. “After achieving all-time low smoking rates, these misleading statements will cost thousands of lives when New Yorkers return to cigarettes.”